Wel, for anyone who's interested I've figured out the problem. It's because I exported the figure and the "dome window" object thing together. Even though I then ungrouped and regrouped everything properly in Bryce, this is what was somehow stuffing up the figure's texture map. When I exported the objects separately and imported them into Bryce separately to reassemble the pic, it worked. This is kind of irritating as I find objects hard to place precisely in Bryce, but I guess I'll get used to it.